equal
deleted
inserted
replaced
11 |
11 |
12 qed_goal "subset_insertI" Set.thy "B <= insert a B" |
12 qed_goal "subset_insertI" Set.thy "B <= insert a B" |
13 (fn _=> [ (rtac subsetI 1), (etac insertI2 1) ]); |
13 (fn _=> [ (rtac subsetI 1), (etac insertI2 1) ]); |
14 |
14 |
15 goal Set.thy "!!x. x ~: A ==> (A <= insert x B) = (A <= B)"; |
15 goal Set.thy "!!x. x ~: A ==> (A <= insert x B) = (A <= B)"; |
16 by (fast_tac set_cs 1); |
16 by (Fast_tac 1); |
17 qed "subset_insert"; |
17 qed "subset_insert"; |
18 |
18 |
19 qed_goal "subset_empty_iff" Set.thy "(A<={}) = (A={})" |
19 qed_goal "subset_empty_iff" Set.thy "(A<={}) = (A={})" |
20 (fn _=> [ (fast_tac (set_cs addIs [equalityI]) 1) ]); |
20 (fn _=> [ (fast_tac (!claset addIs [equalityI]) 1) ]); |
21 |
21 |
22 (*** Big Union -- least upper bound of a set ***) |
22 (*** Big Union -- least upper bound of a set ***) |
23 |
23 |
24 val prems = goal Set.thy |
24 val prems = goal Set.thy |
25 "B:A ==> B <= Union(A)"; |
25 "B:A ==> B <= Union(A)"; |